Determine if the series is convergent.
∑ (((2n^2 + 1)^2)*4^n)/(2(n!))
The Attempt at a Solution
I'n using the Ratio Test and have got as far as (4*(2(n+1)^2+1)^2)/((n+1)((2n^2+1)^2)). I know this series converges but I need to find the limit to be < 1 to show this. Is there way to now divide each term by the dominant term n^2, or do I need to multiply the whole thing out and divide by the new dominant term? I've tried that and have found the limit to be 0/4 = 0.